torovolts (torovolts)

Race #314

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Official speed 90.80 wpm (114.18 seconds elapsed during race)
Without ending ping 91.26 wpm (574 ms delay sending score to TypeRacer’s server)
Timerless 91.67 wpm (507 ms elapsed before first character typed; 113.10 seconds elapsed during race)
Timerless minus one 91.56 wpm, ignoring the first character typed
Race Start May 21, 2024 6:53:40pm UTC
Race Finish May 21, 2024 6:55:34pm UTC
Outcome No win (3 of 5)
Opponents 1. dmaulish (99.96 wpm)
2. mosabreda (96.39 wpm)
Accuracy 96.4%
Points 245.17
Text #4940058 (Length: 864 characters)

Calculus is a tool that helps us understand how a change in one quantity is related to a change in another. How does the speed of a falling object change as a function of time? How does the level of water in a barrel change as a function of the amount of liquid poured into it? We see change occurring in nearly everything we observe in the world and universe, and powerful modern instruments help us see more and more. In this section we introduce the ideas of average and instantaneous rates of change, and show that they are closely related to the slope of a curve at a point P on the curve. We give precise developments of these important concepts in the next chapter, but for now we use an informal approach so you will see how they lead naturally to the main idea of this chapter, the limit. The idea of a limit plays a foundational role throughout calculus.
Characters typed Calculus iss at tool that helps us understand how a change in one quantity is lerelated to a change in another. How does the seppeed of a falling object change as as function of time? How does the leevl vel of water in a barrel change as a afufunction of the amout ofnt of liquid poured into it? We see change occuurrrring eiin enearly everything we observe in the world and universe, and powerful modern instrumentss hel p us see more and mare.ore. In thiss section we indtroduce the ideas of avegarrage and instantanueous rates fo of change, and show tahthat they are clolssely related otto the slope aof a curve at a point P on the curneve. We give precise developments of these important concepts in the next chapter, but fror wnow we use onaanan informal approach so you will see how they aeealdlead naturally to the main idea of this chatpepter, the limit. The idea ofa a limit plays a foundational role throughout calculus.
Timing
Character C a l c u l u s i s s - -s a t - -t t o o
Milliseconds 507 289 173 191 109 67 118 115 133 124 121 115 67 267 89 117 78 97 126 175 90 118 164 128 129
Character l t h a t h e l p s u s u n d e r s t a n
Milliseconds 114 114 186 57 25 65 92 114 137 116 103 118 134 103 148 73 204 109 63 51 103 99 82 86 116
Character d h o w a c h a n g e i n o n e q u a
Milliseconds 58 74 98 81 86 92 75 41 152 35 51 82 49 65 80 90 88 43 299 118 63 66 190 116 59
Character n t i t y i s l e -e -l r e l a t e d t o a
Milliseconds 93 35 99 150 99 112 186 79 70 103 76 229 91 161 35 87 71 82 77 103 120 141 147 75 142
Character c h a n g e i n a n o t h e r . H o w d
Milliseconds 10 106 67 76 101 56 77 80 81 90 66 74 137 50 139 34 28 85 89 122 266 168 106 75 110
Character o e s t h e s e p -p -e p e e d o f a f a
Milliseconds 60 55 48 112 81 78 44 180 379 158 115 176 86 81 60 105 88 113 44 85 69 71 592 129 91
Character l l i n g o b j e c t c h a n g e a s a s
Milliseconds 105 92 75 69 51 46 60 137 171 52 160 118 67 139 57 27 86 61 33 107 125 80 115 83 62
Character -s f u n c t i o n o f t i m e ? H o w d
Milliseconds 430 227 139 196 129 120 153 30 30 120 101 183 269 92 78 65 94 50 229 102 117 244 76 96 76
Character o e s t h e l e e v l - -l -v -e v e l o f
Milliseconds 110 70 15 159 105 44 15 95 90 71 112 7 168 118 263 103 103 121 201 52 95 83 80 69 57
Character w a t e r i n a b a r r e l c h a n g e
Milliseconds 373 61 136 41 144 170 405 117 44 57 77 135 118 129 114 32 327 79 168 17 65 97 53 45 88
Character a s a a f -f -a u -u f u n c t i o n o f t h
Milliseconds 82 399 80 39 111 154 96 282 91 76 369 114 62 83 73 171 58 28 92 111 78 36 80 119 16
Character e a m o u t o f -f -o - -t n t o f l i q u i
Milliseconds 56 37 148 74 68 39 206 123 76 87 449 133 115 111 251 31 96 60 120 103 77 319 184 119 100
Character d p o u r e d i n t o i t ? W e s e e
Milliseconds 130 66 679 78 102 119 239 159 116 134 79 51 56 77 85 96 237 322 163 305 109 82 51 116 160
Character c h a n g e o c c u u r r -r -r -u r r i n g e i
Milliseconds 60 64 107 76 57 86 77 119 95 107 142 117 54 119 235 97 104 180 103 80 95 15 77 134 323
Character -i -e i n e -e n e a r l y e v e r y t h i n g
Milliseconds 182 95 81 108 73 174 288 188 91 40 86 29 96 84 95 77 27 143 65 111 46 35 86 80 59
Character w e o b s e r v e i n t h e w o r l d a
Milliseconds 141 83 36 217 51 360 97 75 157 80 56 128 59 81 86 83 45 165 125 79 121 67 25 127 227
Character n d u n i v e r s e , a n d p o w e r f u l
Milliseconds 88 25 99 243 125 109 89 103 105 77 49 127 114 88 42 45 82 126 80 256 93 87 188 63 87
Character m o d e r n i n s t r u m e n t s s - -s h
Milliseconds 102 409 64 114 70 76 131 78 97 75 113 64 136 116 58 123 55 54 384 120 90 283 97 110 122
Character e l - p u s s e e m o r e a n d m a r
Milliseconds 76 111 299 225 70 95 99 57 168 59 97 135 118 111 36 99 39 58 109 71 40 131 259 82 86
Character e . -. -e -r -a o r e . I n t h i s s - -s s e
Milliseconds 42 184 176 104 107 294 104 82 75 124 254 597 142 121 84 29 56 100 134 161 211 91 130 71 106
Character c t i o n w e i n d -d t r o d u c e t h e
Milliseconds 66 121 61 17 106 115 103 89 111 236 85 116 355 156 29 94 139 103 48 85 62 123 45 35 58
Character i d e a s o f a v e g a r -r -a -g r a g e a n
Milliseconds 139 81 100 24 189 154 153 98 70 95 103 80 90 119 56 172 97 253 182 88 138 43 80 87 95
Character d i n s t a n t a n u -u e o u s r a t e s f
Milliseconds 37 37 221 97 104 17 135 119 24 183 90 210 350 42 102 75 70 238 94 77 136 66 132 89 187
Character o - -o -f o f c h a n g e , a n d s h o w
Milliseconds 49 30 244 93 139 190 62 96 93 51 25 79 60 66 223 155 100 50 56 59 120 32 85 109 108
Character t a h t -t -h -a h a t t h e y a r e c l o l s
Milliseconds 77 82 9 70 419 110 119 163 27 109 111 69 17 81 91 81 108 64 72 33 108 45 84 95 151
Character -s -l s e l y r e l a t e d o t -t -o t o t h e
Milliseconds 165 97 146 72 88 79 90 147 63 190 79 46 91 94 73 98 41 418 111 170 24 127 291 28 346
Character s l o p e a -a o f a c u r v e a t a
Milliseconds 130 87 160 78 66 85 128 118 306 99 68 72 51 86 76 77 108 180 83 65 134 94 122 66 149
Character p o i n t P o n t h e c u r n e -e -n v e .
Milliseconds 119 87 99 88 13 117 256 106 105 79 76 92 30 54 53 104 77 111 162 95 275 106 234 55 116
Character W e g i v e p r e c i s e d e v e l o p m
Milliseconds 121 347 154 9 126 84 88 101 19 146 70 92 84 83 84 73 77 420 78 168 49 173 146 82 194
Character e n t s o f t h e s e i m p o r t a n t c
Milliseconds 95 78 67 196 213 68 93 113 83 43 44 37 75 101 128 84 88 68 60 520 51 55 48 179 232
Character o n c e p t s i n t h e n e x t c h a p t
Milliseconds 112 61 98 177 67 76 84 119 75 56 74 70 50 65 66 90 80 245 176 95 140 63 36 262 156
Character e r , b u t f r -r o r w -w n o w w e u s
Milliseconds 37 120 162 100 111 27 92 44 379 162 260 104 62 96 80 255 141 69 77 94 87 63 81 114 26
Character e o n -n a -a a n -n -a -o a n i n f o r m a l a
Milliseconds 89 44 204 128 224 87 13 136 45 271 226 121 120 63 98 163 90 63 94 88 139 132 101 94 153
Character p p r o a c h s o y o u w i l l s e e h
Milliseconds 80 138 70 127 149 17 118 238 120 45 176 79 76 66 100 139 41 91 113 92 89 64 106 119 128
Character o w t h e y a e -e -a e a l d -d -l -a -e l e a d
Milliseconds 82 102 109 100 52 62 62 108 166 97 131 103 233 26 26 181 302 95 130 118 256 46 38 69 100
Character n a t u r a l l y t o t h e m a i n i d e
Milliseconds 105 71 139 62 111 114 109 101 66 53 139 57 66 328 20 65 83 129 63 53 78 59 133 66 150
Character a o f t h i s c h a t p e -e -p -t p t e r ,
Milliseconds 222 135 152 39 87 161 57 16 117 123 250 55 103 185 99 182 179 214 173 150 68 72 76 72 113
Character t h e l i m i t . T h e i d e a o f a -
Milliseconds 67 59 19 99 77 70 76 38 80 148 198 270 158 153 198 178 94 75 54 89 103 17 195 134 402
Character -a a l i m i t p l a y s a f o u n d a t
Milliseconds 97 183 101 85 164 69 71 50 78 115 146 108 50 50 102 84 62 117 188 123 50 41 36 89 92
Character i o n a l r o l e t h r o u g h o u t c a l
Milliseconds 61 55 95 165 122 91 160 75 100 61 135 255 37 79 133 51 17 343 170 42 80 121 133 86 78
Character c u l u s .
Milliseconds 130 26 311 100 362 101
WPM Timing
Seconds WPM
2.28 57.8
4.57 65.68
6.85 84.07
9.13 94.58
11.42 95.63
13.7 101.59
15.99 98.34
18.27 100.49
20.55 98.09
22.84 99.31
25.12 96.02
27.4 95.9
29.69 92.97
31.97 93.46
34.26 91.78
36.54 90.97
38.82 91.49
41.11 89.04
43.39 90.71
45.67 91.69
47.96 92.58
50.24 93.39
52.53 91.61
54.81 90.86
57.09 89.75
59.38 89.33
61.66 90.5
63.94 90.45
66.23 89.51
68.51 90.2
70.79 90.01
73.08 89.66
75.36 89.33
77.65 90.1
79.93 89.78
82.21 90.2
84.5 90.61
86.78 91.4
89.06 91.35
91.35 90.91
93.63 90.48
95.92 91.08
98.2 90.18
100.48 90.52
102.77 91.08
105.05 90.93
107.33 90.45
109.62 90.75
111.9 91.26
114.18 90.8